{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning the ground-state of a spin model with different Neural Networks available in NetKet\n",
    "\n",
    "The goal of this tutorial is to review various neural network architectures available in NetKet, and this in order to learn the ground-state of a paradigmatic spin model, namely the spin $1/2$ Heisenberg antiferromagnetic spin chain.\n",
    "\n",
    "The Hamiltonian we will consider for this tutorial is the following\n",
    "\n",
    "$$ H = \\sum_{i=1}^{L} \\vec{\\sigma}_{i} \\cdot \\vec{\\sigma}_{i+1}.$$\n",
    "\n",
    "$L$ is the length of the chain, and we will use both open and periodic boundary conditions. $\\vec{\\sigma}=(\\sigma^x,\\sigma^y,\\sigma^z)$ denotes  the vector of Pauli matrices. Please note that there is a factor of $2$ between Pauli-matrices and spin-1/2 operators (thus a factor of $4$ in $H$).\n",
    "\n",
    "We will consider in this tutorial 5 possible ways of determining the ground-state of this model. \n",
    "\n",
    "    0. Defining the Hamiltonian\n",
    "    1. Exact Diagonalization (as a testbed)\n",
    "    2. Starting simple: the Jastrow ansatz\n",
    "    3. Learning with a Restricted Boltzmann Machine (RBM)\n",
    "    4. RBM again, this time with lattice symmetries\n",
    "    5. Learning with Feed Forward Neural Networks\n",
    "    \n",
    "Estimated time for this tutorial: 20 minutes.\n",
    "\n",
    "First things first, let's import the essentials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import netket library\n",
    "import netket as nk\n",
    "# Import Json, this will be needed to examine log files\n",
    "import json\n",
    "# Helper libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0) Defining the Hamiltonian\n",
    "\n",
    "NetKet covers quite a few standard Hamiltonians and lattices, so let's use this to quickly define the antiferromagnetic Heisenberg chain. For the moment we assume $L=22$ and simply define a chain lattice in this way (using periodic boundary conditions for now). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a 1d chain\n",
    "L = 22\n",
    "g = nk.graph.Hypercube(length=L, n_dim=1, pbc=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we need to define the Hilbert space on this graph. We have here spin-half degrees of freedom, and as we know that the ground-state sits in the zero magnetization sector, we can already impose this as a constraint in the Hilbert space. This is not mandatory, but will nicely speeds things up in the following."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the Hilbert space based on this graph\n",
    "# We impose to have a fixed total magnetization of zero \n",
    "hi = nk.hilbert.Spin(s=0.5, graph=g, total_sz=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final element of the triptych is of course the Hamiltonian acting in this Hilbert space, which in our case in already defined in NetKet. Note that the NetKet Hamiltonian uses Pauli Matrices (if you prefer to work with spin-$1/2$ operators, it's pretty trivial to define your own custom Hamiltonian, as covered in another tutorial)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calling the Heisenberg Hamiltonian\n",
    "ha = nk.operator.Heisenberg(hilbert=hi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Exact Diagonalization (as a testbed)\n",
    "\n",
    "Just as a matter of future comparison, let's compute the exact ground-state energy (since this is still possible for $L=22$ using brute-force exact diagonalization).\n",
    "NetKet provides wrappers to the Lanczos algorithm which we now use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The exact ground-state energy is E0= -39.14752260706246\n"
     ]
    }
   ],
   "source": [
    "# compute the ground-state energy (here we only need the lowest energy, and do not need the eigenstate)\n",
    "exact_result = nk.exact.lanczos_ed(ha, first_n=1, compute_eigenvectors=False)\n",
    "exact_gs_energy = exact_result.eigenvalues[0]\n",
    "print('The exact ground-state energy is E0=',exact_gs_energy)\n",
    "\n",
    "# Just in case you can't do this calculation, here is the result\n",
    "# exact_gs_energy = -39.14752260706246"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Starting simple: the Jastrow ansatz\n",
    "\n",
    "Let's start with a simple ansatz for the ground-state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "ma = nk.machine.Jastrow(hilbert=hi)\n",
    "ma.init_random_parameters(seed=1, sigma=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "### Jastrow calculation\n",
      "Has 231 parameters\n",
      "The Jastrow calculation took 15.655055046081543 seconds\n"
     ]
    }
   ],
   "source": [
    "# Optimizer\n",
    "op = nk.optimizer.Sgd(learning_rate=0.1)\n",
    "\n",
    "# Sampler\n",
    "sa = nk.sampler.MetropolisExchange(machine=ma,graph=g)\n",
    "ma.init_random_parameters(seed=12, sigma=0.01)\n",
    "\n",
    "# Stochastic reconfiguration\n",
    "gs = nk.variational.Vmc(\n",
    "    hamiltonian=ha,\n",
    "    sampler=sa,\n",
    "    optimizer=op,\n",
    "    n_samples=1000,\n",
    "    diag_shift=0.1,\n",
    "    method='Sr')\n",
    "\n",
    "start = time.time()\n",
    "gs.run(output_prefix='Jastrow', n_iter=300)\n",
    "end = time.time()\n",
    "\n",
    "print('### Jastrow calculation')\n",
    "print('Has',ma.n_par,'parameters')\n",
    "print('The Jastrow calculation took',end-start,'seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import the data from log file\n",
    "data=json.load(open(\"Jastrow.log\"))\n",
    "\n",
    "# Extract the relevant information\n",
    "iters_Jastrow=[]\n",
    "energy_Jastrow=[]\n",
    "\n",
    "for iteration in data[\"Output\"]:\n",
    "    iters_Jastrow.append(iteration[\"Iteration\"])\n",
    "    energy_Jastrow.append(iteration[\"Energy\"][\"Mean\"])\n",
    "    \n",
    "fig, ax1 = plt.subplots()\n",
    "ax1.plot(iters_Jastrow, energy_Jastrow, color='C8', label='Energy (Jastrow)')\n",
    "ax1.set_ylabel('Energy')\n",
    "ax1.set_xlabel('Iteration')\n",
    "plt.axis([0,iters_Jastrow[-1],exact_gs_energy-0.1,exact_gs_energy+0.4])\n",
    "plt.axhline(y=exact_gs_energy, xmin=0,\n",
    "                xmax=iters_Jastrow[-1], linewidth=2, color='k', label='Exact')\n",
    "ax1.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well that's not too bad for a simple ansatz. But we can do better, can't we?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Learning with a Restricted Boltzmann Machine (RBM)\n",
    "\n",
    "We will now consider another celebrated ansatz, the Restricted Boltzmann Machine (RBM). It simply consists of two layers: a visible one representing the $L$ spin 1/2 degrees of freedom, and an hidden one which contains a different number $M$ of hidden units. There are connections between all visible and hidden nodes. The ansatz is the [following](https://www.netket.org/docs/machine_RbmSpin/)\n",
    "\n",
    "$\\Psi_{\\rm RBM} (\\sigma_1^z,\\sigma_2^z, ..., \\sigma_L^z)  = \\exp ( \\sum_{i=1}^L a_i \\sigma_i^z ) \\prod_{i=1}^M \\cosh (b_i + \\sum_j W_{ij} \\sigma^z_j)$ \n",
    "\n",
    "$a_i$ (resp. $b_i$) are the visible (resp. hidden) bias. Together with the weights $W_{ij}$, they are variational parameters that we (or rather NetKet) will optimize to minimize the energy. Netket gives you the control on the important parameters in this ansatz, such as $M$ and the fact that you want to use or not the biases. The full explanation is [here](https://www.netket.org/docs/machine_RbmSpin/). \n",
    "\n",
    "More conveniently (especially if you want to try another $L$ in this tutorial), let's define the hidden unit density $\\alpha = M / L$, and invoke the RBM ansatz in NetKet with as many hidden as visible units. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "# RBM ansatz with alpha=1\n",
    "ma = nk.machine.RbmSpin(alpha=1, hilbert=hi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let us use the same sampler (Metropolis exchange) with some different random initial parameters, optimizer (stochastic gradient), and variational method (stochastic reconfiguration) as for the Jastrow ansatz, and let's run things!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "### RBM calculation\n",
      "Has 528 parameters\n",
      "The RBM calculation took 79.31553912162781 seconds\n"
     ]
    }
   ],
   "source": [
    "# Sampler\n",
    "sa = nk.sampler.MetropolisExchange(machine=ma,graph=g)\n",
    "ma.init_random_parameters(seed=123, sigma=0.01)\n",
    "\n",
    "# Optimizer\n",
    "op = nk.optimizer.Sgd(learning_rate=0.05)\n",
    "# Stochastic reconfiguration\n",
    "gs = nk.variational.Vmc(\n",
    "    hamiltonian=ha,\n",
    "    sampler=sa,\n",
    "    optimizer=op,\n",
    "    n_samples=1000,\n",
    "    diag_shift=0.1,\n",
    "    use_iterative=True,\n",
    "    method='Sr')\n",
    "\n",
    "start = time.time()\n",
    "gs.run(output_prefix='RBM', n_iter=600)\n",
    "end = time.time()\n",
    "\n",
    "print('### RBM calculation')\n",
    "print('Has',ma.n_par,'parameters')\n",
    "print('The RBM calculation took',end-start,'seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import the data from log file\n",
    "data=json.load(open(\"RBM.log\"))\n",
    "\n",
    "# Extract the relevant information\n",
    "iters=[]\n",
    "energy_RBM=[]\n",
    "\n",
    "for iteration in data[\"Output\"]:\n",
    "    iters.append(iteration[\"Iteration\"])\n",
    "    energy_RBM.append(iteration[\"Energy\"][\"Mean\"])\n",
    "    \n",
    "fig, ax1 = plt.subplots()\n",
    "ax1.plot(iters_Jastrow, energy_Jastrow, color='C8', label='Energy (Jastrow)')\n",
    "ax1.plot(iters, energy_RBM, color='red', label='Energy (RBM)')\n",
    "ax1.set_ylabel('Energy')\n",
    "ax1.set_xlabel('Iteration')\n",
    "plt.axis([0,iters[-1],exact_gs_energy-0.03,exact_gs_energy+0.2])\n",
    "plt.axhline(y=exact_gs_energy, xmin=0,\n",
    "                xmax=iters[-1], linewidth=2, color='k', label='Exact')\n",
    "ax1.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that this plot zooms closer to the exact ground-state energy. With 600 iterations, we start to see convergence and reach the ground-state energy within about one per thousand, this is already nice! But we are not totally there yet, and in particular the simpler (less parameters) Jastrow wave-function seems to perform better for this example. How can we improve things? As an exercice, try to increase the number of hidden units and/or the number of iterations. What is happening? You can also check out the influence of the learning rate. \n",
    "\n",
    "By playing with these parameters, you have hopefully arrived at an improved result, but likely at an increased CPU time cost. Let's do things differently, and take to our advantage the symmetries of the Hamiltonian in the neural network construction. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. RBM again, this time with lattice symmetries\n",
    "\n",
    "Let's define a similar RBM machine, which takes into account that the model has translational symmetries. All sites are equivalent and thus many of the wave-functions coefficients are related by symmetry. We use the same exact hyperparameters as in the previous RBM calculation ($\\alpha=1$, same learning rate, and number of samples and iterations in the Variational Monte Carlo) and run now a symmetric RBM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "### Symmetric RBM calculation\n",
      "Has 24 parameters\n",
      "The Symmetric RBM calculation took 33.651692152023315 seconds\n"
     ]
    }
   ],
   "source": [
    "# Symmetric RBM Spin Machine\n",
    "ma = nk.machine.RbmSpinSymm(alpha=1, hilbert=hi)\n",
    "ma.init_random_parameters(seed=1234, sigma=0.01)\n",
    "\n",
    "# Metropolis Exchange Sampling\n",
    "# Notice that this sampler exchanges two neighboring sites\n",
    "# thus preservers the total magnetization\n",
    "sa = nk.sampler.MetropolisExchange(machine=ma, graph=g)\n",
    "\n",
    "# Optimizer\n",
    "op = nk.optimizer.Sgd(learning_rate=0.05)\n",
    "\n",
    "# Stochastic reconfiguration\n",
    "gs = nk.variational.Vmc(\n",
    "    hamiltonian=ha,\n",
    "    sampler=sa,\n",
    "    optimizer=op,\n",
    "    n_samples=1000,\n",
    "    diag_shift=0.1,\n",
    "    use_iterative=True,\n",
    "    method='Sr')\n",
    "\n",
    "start = time.time()\n",
    "gs.run(output_prefix='RBMSymmetric', n_iter=300)\n",
    "end = time.time()\n",
    "\n",
    "print('### Symmetric RBM calculation')\n",
    "print('Has',ma.n_par,'parameters')\n",
    "print('The Symmetric RBM calculation took',end-start,'seconds')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulation was much faster, wasn't it? There were of course much less parameters to optimize. Now let's extract the results and plot them using a zoomed scale, and together with the previous results with the RBM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import the data from log file\n",
    "data=json.load(open(\"RBMSymmetric.log\"))\n",
    "\n",
    "# Extract the relevant information\n",
    "energy_symRBM=[]\n",
    "iters_symRBM=[]\n",
    "for iteration in data[\"Output\"]:\n",
    "    energy_symRBM.append(iteration[\"Energy\"][\"Mean\"])\n",
    "    iters_symRBM.append(iteration[\"Iteration\"])\n",
    "    \n",
    "fig, ax1 = plt.subplots()\n",
    "ax1.plot(iters_Jastrow, energy_Jastrow, color='C8', label='Energy (Jastrow)')\n",
    "ax1.plot(iters, energy_RBM, color='red', label='Energy (RBM)')\n",
    "ax1.plot(iters_symRBM, energy_symRBM, color='blue', label='Energy (Symmetric RBM)')\n",
    "\n",
    "ax1.set_ylabel('Energy')\n",
    "ax1.set_xlabel('Iteration')\n",
    "plt.axis([0,iters_symRBM[-1],exact_gs_energy-0.06,exact_gs_energy+0.12])\n",
    "plt.axhline(y=exact_gs_energy, xmin=0,\n",
    "                xmax=iters[-1], linewidth=2, color='k', label='Exact')\n",
    "ax1.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not only the simulation was faster in terms of CPU time, but we are now reaching the ground-state in a much lower number of iterations! Imposing symmetries greatly helps, and NetKet allows to do this. Note that there is also a symmetric version of the Jastrow ansatz that we tested [earlier](#2.-Starting-simple:-the-Jastrow-ansatz) in NetKet, which is called `JastrowSymm`. As an exercice, check it out. What you will find is that while it converges slightly faster in terms of iterations with respect to the non-symmetric Jastrow, it does not improve the estimate of the ground-state energy. We actually see that the symmetric RBM sets the standard very high."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Learning with Feed Forward Neural Networks\n",
    "\n",
    "Now let's try a more complex network, namely a Feed Forward Neural Network (FFNN). There you will have more freedom to construct your own specific architecture. We'll try two different FFNN in this tutorial.\n",
    "\n",
    "The first one is a simple structure: the first layer takes as input L-dimensional input, applies a bias and outputs two times more data, just followed by a `Lncosh` activation layer. The final layer `SumOuput` is needed to obtain a single number for the wave-function coefficient associated to the input basis state.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "### Feed Forward calculation\n",
      "Has 1012 parameters\n",
      "The Feed Forward calculation took 100.12213611602783 seconds\n"
     ]
    }
   ],
   "source": [
    "layers = (nk.layer.FullyConnected(input_size=L,output_size=int(2*L),use_bias=True),\n",
    "          nk.layer.Lncosh(input_size=int(2*L)),\n",
    "          nk.layer.SumOutput(input_size=int(2*L))\n",
    "         )\n",
    "for layer in layers:\n",
    "    layer.init_random_parameters(seed=12345, sigma=0.01)\n",
    "    \n",
    "ffnn = nk.machine.FFNN(hi, layers)\n",
    "\n",
    "sa = nk.sampler.MetropolisExchange(graph=g, machine=ffnn)\n",
    "\n",
    "opt = nk.optimizer.Sgd(learning_rate=0.05)\n",
    "\n",
    "gs = nk.variational.Vmc(hamiltonian=ha,\n",
    "                        sampler=sa,\n",
    "                        optimizer=opt,\n",
    "                        n_samples=1000,\n",
    "                        use_iterative=True,\n",
    "                        method='Sr')\n",
    "\n",
    "start = time.time()\n",
    "gs.run(output_prefix='FF', n_iter=300)\n",
    "end = time.time()\n",
    "\n",
    "print('### Feed Forward calculation')\n",
    "print('Has',ffnn.n_par,'parameters')\n",
    "print('The Feed Forward calculation took',end-start,'seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import the data from log file\n",
    "data=json.load(open(\"FF.log\"))\n",
    "\n",
    "# Extract the relevant information\n",
    "energy_FF=[]\n",
    "for iteration in data[\"Output\"]:\n",
    "    energy_FF.append(iteration[\"Energy\"][\"Mean\"])\n",
    "    \n",
    "fig, ax1 = plt.subplots()\n",
    "ax1.plot(iters_Jastrow, energy_Jastrow, color='C8',linestyle=\"None\", marker='d',label='Energy (Jastrow)')\n",
    "ax1.plot(iters, energy_RBM, color='red', marker='o',linestyle=\"None\",label='Energy (RBM)')\n",
    "ax1.plot(iters_symRBM, energy_symRBM, color='blue',linestyle=\"None\",marker='o',label='Energy (Symmetric RBM)')\n",
    "ax1.plot(iters_symRBM, energy_FF, color='orange', marker='s',linestyle=\"None\",label='Energy (Feed Forward, take 1)')\n",
    "ax1.legend(bbox_to_anchor=(1.05, 0.3))\n",
    "ax1.set_ylabel('Energy')\n",
    "ax1.set_xlabel('Iteration')\n",
    "plt.axis([0,iters_symRBM[-1],exact_gs_energy-0.02,exact_gs_energy+0.1])\n",
    "plt.axhline(y=exact_gs_energy, xmin=0,\n",
    "                xmax=iters[-1], linewidth=2, color='k', label='Exact')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are clearly better than a simple (non-symmetrized RBB), and perform slightly better than the Jastrow ansatz. Let us increase the number of layers by adding a fully-connected layer with bias and  `Lncosh` activation (with $2L$ inputs and ouputs) before the final `SumOuput` layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "### Feed Forward (more layers) calculation\n",
      "Has 2992 parameters\n",
      "The Feed Forward (more layers) calculation took 285.4591450691223 seconds\n"
     ]
    }
   ],
   "source": [
    "layers = (nk.layer.FullyConnected(input_size=L,output_size=int(2*L),use_bias=True),\n",
    "          nk.layer.Lncosh(input_size=int(2*L)),\n",
    "          nk.layer.FullyConnected(input_size=int(2*L),output_size=int(2*L),use_bias=True),\n",
    "          nk.layer.Lncosh(input_size=int(2*L)),\n",
    "          nk.layer.SumOutput(input_size=int(2*L)),\n",
    "         )\n",
    "for layer in layers:\n",
    "    layer.init_random_parameters(seed=123456, sigma=0.01)\n",
    "    \n",
    "ffnn = nk.machine.FFNN(hi, layers)\n",
    "\n",
    "sa = nk.sampler.MetropolisExchange(graph=g, machine=ffnn)\n",
    "\n",
    "opt = nk.optimizer.Sgd(learning_rate=0.05)\n",
    "\n",
    "gs = nk.variational.Vmc(hamiltonian=ha,\n",
    "                        sampler=sa,\n",
    "                        optimizer=opt,\n",
    "                        n_samples=1000,\n",
    "                        use_iterative=True,\n",
    "                        method='Sr')\n",
    "\n",
    "start = time.time()\n",
    "gs.run(output_prefix='FF2', n_iter=300)\n",
    "end = time.time()\n",
    "\n",
    "\n",
    "print('### Feed Forward (more layers) calculation')\n",
    "print('Has',ffnn.n_par,'parameters')\n",
    "print('The Feed Forward (more layers) calculation took',end-start,'seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import the data from log file\n",
    "data=json.load(open(\"FF2.log\"))\n",
    "\n",
    "# Extract the relevant information\n",
    "energy_FF_morelayers=[]\n",
    "for iteration in data[\"Output\"]:\n",
    "    energy_FF_morelayers.append(iteration[\"Energy\"][\"Mean\"])\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "#ax1.plot(iters_Jastrow, energy_Jastrow, color='C8',linestyle=\"None\", marker='d',label='Energy (Jastrow)')\n",
    "#ax1.plot(iters, energy_RBM, color='red', label='Energy (RBM)')\n",
    "ax1.plot(iters_symRBM, energy_symRBM, color='blue',linestyle=\"None\",marker='o',label='Energy (Symmetric RBM)')\n",
    "ax1.plot(iters_symRBM, energy_FF, color='orange', marker='s',alpha=0.5,linestyle=\"None\",label='Energy (Feed Forward, take 1)')\n",
    "ax1.plot(iters_symRBM, energy_FF_morelayers, color='green',marker='s',linestyle=\"None\", alpha=1,label='Energy (Feed Forward, more layers)')\n",
    "ax1.legend(bbox_to_anchor=(1.05, 0.5))\n",
    "ax1.set_ylabel('Energy')\n",
    "ax1.set_xlabel('Iteration')\n",
    "plt.axis([0,iters_symRBM[-1],exact_gs_energy-0.02,exact_gs_energy+0.06])\n",
    "plt.axhline(y=exact_gs_energy, xmin=0,\n",
    "                xmax=iters[-1], linewidth=2, color='k', label='Exact')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are even better, but at the price of an increase in computational time....\n",
    "\n",
    "Note that more complex structures, such as Convolutional Neural Networks (CNN), can also be used within Netket. However, for such 1d systems, they do not bring too much compared to the symmetric RBM (as a matter of fact, the symmetric RBM is a special type of a simple CNN. CNNs show their full strength for more complex systems, such as 2d quantum systems. Convolutional Neural Networks will be the topic of another tutorial in NetKet (and we'll make there the connection with the special case of the symmetric RBM). \n",
    "\n",
    "Finally let us conclude that another type of machine, Matrix Product States (MPS), is also available in NetKet. They do perform extremely well for 1d quantum systems. Since however they are a bit different, they will be presented in another tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
